
By taking the boundary conditions (REF )
into account, one finds that the formal change of the Hamiltonian
functional \({H}\)  follows to \(\dot{{H}}=\int _{0}^{L}g(z)\frac{p}{\rho }u\mathrm {d}z\) ,
i.e. we have a distributed port that can be used for control purposes.
In fact, for the system under consideration, in [1]}
a dynamic controller based on the energy-Casimir method has been designed.
However, with regard to this control methodology, it should be mentioned
that it yields unsatisfactory results for uncertain initial conditions,
see e.g. [2]} where this problem is briefly discussed
for a boundary-control system. Therefore, in the following we intend
to design an infinite-dimensional observer in order to overcome this
obstacle.
